For each of the given triangles, determine if there is enough information to find all the remaining sides and angles in the triangle using only the sine rule:
Three sides are known:
Two of the angles and the side included between them are known:
Two of the angles and a side not included between them are known:
Two of the sides and an angle included between them are known:
Solve the following equations for x, given that all equations relate to acute-angled triangles. Round your answers to two decimal places.
\dfrac{x}{\sin 78 \degree} = \dfrac{50}{\sin 43 \degree}
\dfrac{11}{\sin 66 \degree} = \dfrac{x}{\sin 34 \degree}
\dfrac{\sin 78 \degree}{20} = \dfrac{\sin x}{13}
\dfrac{5}{\sin x} = \dfrac{7}{\sin 70 \degree}
\dfrac{22}{\sin x} = \dfrac{31}{\sin 66 \degree}
For each of the following triangles, write an equation relating the sides and angles using the sine rule:
For each of the following triangles:
Find the value of a using the sine rule. Round your answer to two decimal places.
Use another trigonometric ratio and the fact that the triangle is right-angled to calculate and confirm the value of a. Round your answer to two decimal places.
For each of the following triangles, find the side length a using the sine rule. Round your answers to two decimal places.
For each of the following triangles, find the length of side x, correct to one decimal place:
Consider the following triangle:
Find the length of side HK to two decimal places.
Find the length of side KJ to two decimal places.
Consider the triangle ABC, where BC = 37.8 \text{ m} , \angle BAC = 57 \degree and \angle ACB = 42 \degree.
Calculate the length of side AB, correct to two decimal places.
Consider the triangle PQR, where QR = 4.79 \text{ mm}, \angle QPR = 33 \degree and \angle PRQ = 124 \degree.
Calculate the length of side PQ, correct to two decimal places.
Consider the triangle ABC with \angle C = 72.53 \degree and \angle B = 31.69 \degree, and one side length \\ a = 5.816\text{ m}.
Find \angle A. Round your answer to two decimal places.
Find the length of side b. Round your answer to three decimal places.
Find the length of side c. Round your answer to three decimal places.
Consider the given triangle:
Write out the sine rule to find h.
Find the value of h to two decimal places.
Consider the triangle MNP, where NP = 100 \text{ m} , MN = 204 \text{ m} and \angle NPM = 58 \degree.
Calculate the size of the acute angle \angle NMP, correct to the nearest minute.
For each of the following acute angled triangles, calculate the size of angle B to the nearest degree:
\triangle ABC where \angle A = 57 \degree side a = 156 \text{ cm} and side b = 179 \text{ cm}
\triangle ABC where \angle A = 48 \degree side a = 2.7 \text{ cm} and side b = 1.9 \text{ cm}
For each of the following diagrams, find the size of the angle x. Round your answers to one decimal place.
